Characteristics and evolution of the in-situ stress field have a significant influence over reservoir's formation, type and hydrocarbon distribution. The status of in-situ stress, especially the tectonic stress, has also a dominant effect on reservoir development, such as wellbore stability, hydraulic fracturing, sanding production, reservoir depletion process, casing failure and surface subsidence, et al. Analysis of the tectonic stress is, therefore, of great importance to reservoir studies.
Today's technologies allow us to model the rock mass and geological reservoir in-situ stress using 3D numerical modeling tools, in which the geological structure can be modeled by discrete elements or grids, and the tectonic activities/thermal stress by applying appropriate boundary loading conditions. Once the tectonic boundary conditions have been determined, it will be a simple matter to compute the in-situ stress field using the numerical model. However, how to invert the loading boundary from the measured data and field information is still one of the most difficult issues in the industry.
One of the big challenges for in-situ stress modeling comes from the complexity of in-situ stress itself. First of all, the in-situ stress was formed from its initial state of loose sediment to its present geological state which has undergone a long and complicated process, such as overburden deposition, repeated cycles of elevation and depression, tectonic forces and thermal effects. Furthermore, the mechanical erosions and thermal histories of the site under investigation may be complex, leading to additional loading path dependent sources of distortion of the in-situ stress field. Lastly, rock is rarely well represented by a homogeneous isotropic continuum medium as assumed in most of the geomechanical models.
Currently there are a few ways to approach the issue, but those ways have their own limitation. For example, “Integrated Stress Determination Approach” relies on a nonlinear least squares approach to determine the regional stress field based on local stress measurement, but the strong assumptions involved in the ISDA method, such as neglecting the lateral variations of stress and the rotation of the principal stress direction, restrain this model applicability in complex geological conditions. See, e.g., D. A S K, New Developments in the Integrated Stress Determination Method and Their Application to Rock Stress Data at the Äspö HRL, Sweden, International Journal of Rock Mechanics & Mining Sciences, 14 Apr. 2005, Page 1-20.
In addition, A. Ledesma et al proposed a probabilistic framework to perform inverse analysis of geotechnical problems. The formulation allows the incorporation of existing prior information on the parameters in a consistent way. The method is based on the maximum likelihood approach that allows a straightforward introduction of the uncertainties measurements and prior information. However this approach is based on the mathematical optimization theory and doses not include the complex geological mechanisms in the model. See, A. LEDESMA, A. GENS, E. E. ALONSO, Parameter and Variance Estimation in Geotechnical Backanalysis Using Prior Information, International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 20, 1996, Page 119-141.
Further, F. Tonon et al addressed an estimation of boundary conditions for rock mass by means of Bayesian identification procedures. See, F. TONON, B. AMADEI, E. PAN, D. M. FRANGOPOL, Bayesian Estimation of Rock Mass Boundary Conditions with Applications to the AECL Underground Research Laboratory, International Journal of Rock Mechanics & Mining Sciences, 22 Jun. 2001, Page 995-1027. In Tonon's paper, the estimation of boundary conditions for rock mass models is addressed by means of Bayesian identification procedures. For linearly elastic rock masses, the boundary conditions are computed in a one-step solution. For rock masses with non-linear behavior, an iterative procedure must be followed. However, the uniform boundary conditions assumed in the model can not meet the requirement of complex geological conditions.
Additionally, S. D. McKinnon focused on stress input modification to account for the incorrect rock modulus resulting from strain measurement in his work. See, S. D. MCKINNON, Analysis of Stress Measurements Using A Numerical Model Methodology, International Journal of Rock Mechanics & Mining Sciences, 12 Jul. 2001, Page 699-709. McKinnon described a method that enables the boundary conditions of numerical models to be calibrated to individual or groups of stress measurements. The stress field at any point is assumed to be comprised of gravitational and tectonic components. The tectonic component is assumed to act entirely in the horizontal plane in the far-field and at the model boundary. Unit normal and shear tractions are applied to the model boundaries and the response is computed at the location of the measurement points in the model. An optimization procedure is used to compute the proportions of each unit response tensor that is required, in addition to the gravitational stress, to reproduce the measured stress at the measurement point in the model. However, same as F. Tonon's approach, McKinnon uses the uniform far-field boundary conditions, which is not the case for most geological structures